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In the demonstration of a stunt, two solid balls of equal density and radii rand 2, are placed with the centre of the larger one above the middle of a cart of mass M = 6 kg andlength L = 3 m. The mass of the smaller ball is m = 1 kg. The balls are made to roll,without slipping in such a way that a straight line connecting their centres remains ata constant angle 0) = 53° to the horizontal. The cart is pulled by a horizontal force. Findthetimetaken for the balls to fall of the edge of the cart, in seconds(Take g = 10 m/s) |
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Answer» tion:Given,Two balls, each of radius R and of equal mass and density, are placed in contact.Step-1:FIND the Distance between the centre of two ballsDistance between the centre of two balls = SUM of their Radii.Distance between the centre of two balls =R+R=2R.Step-2:Express the Mass of a ball as product of Density and Volume.(This would be same for other ball ,given that two balls have equal mass)Since, the shape of the ball is Sphere.Volume of the ball V=34πR3So,Mass of the ball m=ρ×34πR3Step-3:Find the force of gravitation between the two balls.According to Newton's LAW of Universal GravitationF=r2GMmWhere,F= Gravitational Force between two objects.G= Gravitational constantM= Mass of the first objectm= Mass of the SECOND objectr= Distance between objectsHere,.M=m=ρ×34πR3Substituting Values⟹F=(2R)2Gm2⟹F=4R2G(ρ×34πR3)2⟹F=G×ρ2×(34)2×41×R2 |
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